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Algebraic Signed Graphs: A Review
Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020
The field of graph theory has undergone incredible development during the past century and during the past quarter-century, the revolution of the subject has continued, with individual areas (such as algebraic combinatorics, algorithmic graph theory) escalating to the point of having essential sub-branches themselves. Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra in diverse combinatorial contexts and vice versa. Associating a graph with an algebraic structure is a research subject in this area and has attracted huge attention. In fact, research in this subject aims at exploring the relationship between algebra and graph theory and their applications.
Degenerate 2D bivariate Appell polynomials: properties and applications
Published in Applied Mathematics in Science and Engineering, 2023
Shahid Ahmad Wani, Arundhati Warke, Javid Gani Dar
Polynomial sequences are of interest in enumerative combinatorics, algebraic combinatorics, and applied mathematics. The Laguerre polynomials, Chebyshev polynomials, Legendre polynomials, and Jacobi polynomials are a few polynomial sequences that appear as solutions to particular ordinary differential equations in physics and approximation theory. The most significant polynomial sequences is a class of Appell polynomial sequences [1]. Many applications of the Appell polynomial sequence may be found in theoretical physics, approximation theory, mathematics, and related fields of mathematics. The set of all Appell sequences is closed as a result of umbral polynomial sequence composition. This process turns the collection of all Appell sequences into an abelian group.
Special Issue dedicated to Workshop on Graph Spectra, Combinatorics and Optimization (WGSCO2018)
Published in Optimization, 2020
Rosalind Elster, Tatiana Tchemisova, Gerhard-Wilhelm Weber
The topics of the Workshop reflected the diversity of the scientific interests of Prof. Domingos M. Cardoso and the main lines of research of the Group on Graph Theory, Optimization and Combinatorics, which had been coordinated by him during many years within the Research Unit CIDMA of the Mathematics Department of the University of Aveiro: Algebraic Combinatorics, Algebraic Graph Theory, Algorithms and Computing Techniques, Combinatorial Optimization, Communications and Control Theory, Enumerative and Extremal Combinatorics, Graph Theory, Optimization in Graphs, Graph Spectra and Applications, Linear Optimization, Networks, Nonlinear Optimization, and others.